Symmetry

25 pages, 704 KiB

Open AccessArticle

Novel Three-Way Decisions Models with Multi-Granulation Rough Intuitionistic Fuzzy Sets

by Zhan-Ao Xue^1,2,*, Dan-Jie Han^1,2,*, Min-Jie Lv^1,2 and Min Zhang^1,2

¹ College of Computer and Information Engineering, Henan Normal University, Xinxiang 453007, China

² Engineering Lab of Henan Province for Intelligence Business & Internet of Things, Henan Normal University, Xinxiang 453007, China

Symmetry 2018, 10(11), 662; https://doi.org/10.3390/sym10110662 - 21 Nov 2018

Cited by 10 | Viewed by 3105

Abstract

The existing construction methods of granularity importance degree only consider the direct influence of single granularity on decision-making; however, they ignore the joint impact from other granularities when carrying out granularity selection. In this regard, we have the following improvements. First of all, [...] Read more.

The existing construction methods of granularity importance degree only consider the direct influence of single granularity on decision-making; however, they ignore the joint impact from other granularities when carrying out granularity selection. In this regard, we have the following improvements. First of all, we define a more reasonable granularity importance degree calculating method among multiple granularities to deal with the above problem and give a granularity reduction algorithm based on this method. Besides, this paper combines the reduction sets of optimistic and pessimistic multi-granulation rough sets with intuitionistic fuzzy sets, respectively, and their related properties are shown synchronously. Based on this, to further reduce the redundant objects in each granularity of reduction sets, four novel kinds of three-way decisions models with multi-granulation rough intuitionistic fuzzy sets are developed. Moreover, a series of concrete examples can demonstrate that these joint models not only can remove the redundant objects inside each granularity of the reduction sets, but also can generate much suitable granularity selection results using the designed comprehensive score function and comprehensive accuracy function of granularities. Full article

(This article belongs to the Special Issue Discrete Mathematics and Symmetry)

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14 pages, 1367 KiB

Open AccessArticle

1, 2, 3, Many—Perceptual Integration of Motif Repetitions

by Mikhail Katkov^*

, Hila Harris and Dov Sagi

Department of Neurobiology, Weizmann Institute of Science, Rehovot 76100, Israel

Symmetry 2018, 10(11), 661; https://doi.org/10.3390/sym10110661 - 21 Nov 2018

Viewed by 2988

Abstract

It is generally assumed that the initial integration of visual information is limited in its spatial extent. Of particular interest is the extent to which image symmetries are detected and integrated. Here we studied the spatial extent of visual integration in textures constructed [...] Read more.

It is generally assumed that the initial integration of visual information is limited in its spatial extent. Of particular interest is the extent to which image symmetries are detected and integrated. Here we studied the spatial extent of visual integration in textures constructed from wallpaper symmetry groups. Using tools from statistical physics, we obtained images ranging from symmetric ones to completely random ones, whereas the textural elements were of the same quality. Results show that the psychometric curves for 3 × 3 motif repetitions are similar to those of images having more repetitions, whereas an equivalent physical scaling of the images does not alter the performance. Full article

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30 pages, 23429 KiB

Open AccessArticle

Multiple-Image Encryption Algorithm Based on the 3D Permutation Model and Chaotic System

by Xiaoqiang Zhang

and Xuesong Wang^*

School of Information and Control Engineering, China University of Mining and Technology, Xuzhou 221116, China

Symmetry 2018, 10(11), 660; https://doi.org/10.3390/sym10110660 - 20 Nov 2018

Cited by 24 | Viewed by 4699

Abstract

Large numbers of images are produced in many fields every day. The content security of digital images becomes an important issue for scientists and engineers. Inspired by the magic cube game, a three-dimensional (3D) permutation model is established to permute images, which includes [...] Read more.

Large numbers of images are produced in many fields every day. The content security of digital images becomes an important issue for scientists and engineers. Inspired by the magic cube game, a three-dimensional (3D) permutation model is established to permute images, which includes three permutation modes, i.e., internal-row mode, internal-column mode, and external mode. To protect the image content on the Internet, a novel multiple-image encryption symmetric algorithm (block cipher) with the 3D permutation model and the chaotic system is proposed. First, the chaotic sequences and chaotic images are generated by chaotic systems. Second, the sender permutes the plain images by the 3D permutation model. Lastly, the sender performs the exclusive OR operation on permuted images. The simulation and algorithm comparisons display that the proposed algorithm possesses desirable encryption images, high security, and efficiency. Full article

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19 pages, 4202 KiB

Open AccessArticle

A New Radar Signal Recognition Method Based on Optimal Classification Atom and IDCQGA

by Jian Wan, Guoqing Ruan^*

, Qiang Guo and Xue Gong

College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China

Symmetry 2018, 10(11), 659; https://doi.org/10.3390/sym10110659 - 20 Nov 2018

Cited by 3 | Viewed by 3472

Abstract

Radar electronic reconnaissance is an important part of modern and future electronic warfare systems and is the primary method to obtain non-cooperative intelligence information. As the task requirement of radar electronic reconnaissance, it is necessary to identify the non-cooperative signals from the mixed [...] Read more.

Radar electronic reconnaissance is an important part of modern and future electronic warfare systems and is the primary method to obtain non-cooperative intelligence information. As the task requirement of radar electronic reconnaissance, it is necessary to identify the non-cooperative signals from the mixed signals. However, with the complexity of battlefield electromagnetic environment, the performance of traditional recognition system is seriously affected. In this paper, a new recognition method based on optimal classification atom and improved double chains quantum genetic algorithm (IDCQGA) is researched, optimal classification atom is a new feature for radar signal recognition, IDCQGA with symmetric coding performance can be applied to the global optimization algorithm. The main contributions of this paper are as follows: Firstly, in order to measure the difference of multi-class signals, signal separation degree based on distance criterion is proposed and established according to the inter-class separability and intra-class aggregation of the signals. Then, an IDCQGA is proposed to select the best atom for classification under the constraint of distance criterion, and the inner product of the signal and the best atom for classification is taken as the eigenvector. Finally, the extreme learning machine (ELM) is introduced as classifier to complete the recognition of signals. Simulation results show that the proposed method can improve the recognition rate of multi-class signals and has better processing ability for overlapping eigenvector parameters. Full article

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Graphical abstract

37 pages, 538 KiB

Open AccessArticle

Triangular Cubic Hesitant Fuzzy Einstein Hybrid Weighted Averaging Operator and Its Application to Decision Making

by Aliya Fahmi¹, Fazli Amin¹, Florentin Smarandache²

, Madad Khan³ and Nasruddin Hassan^4,*

¹ Department of Mathematics, Hazara University Mansehra, Dhodial 21130, Pakistan

² Department of Mathematics, University of New Mexico, Albuquerque, NM 87301, USA

³ Department of Mathematics, Comsats University Abbottabad, Abbottabad 22010, Pakistan

⁴ School of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, UKM Bangi Selangor DE 43600, Malaysia

Symmetry 2018, 10(11), 658; https://doi.org/10.3390/sym10110658 - 20 Nov 2018

Cited by 24 | Viewed by 3592

Abstract

In this paper, triangular cubic hesitant fuzzy Einstein weighted averaging (TCHFEWA) operator, triangular cubic hesitant fuzzy Einstein ordered weighted averaging (TCHFEOWA) operator and triangular cubic hesitant fuzzy Einstein hybrid weighted averaging (TCHFEHWA) operator are proposed. An approach to multiple attribute group decision making [...] Read more.

In this paper, triangular cubic hesitant fuzzy Einstein weighted averaging (TCHFEWA) operator, triangular cubic hesitant fuzzy Einstein ordered weighted averaging (TCHFEOWA) operator and triangular cubic hesitant fuzzy Einstein hybrid weighted averaging (TCHFEHWA) operator are proposed. An approach to multiple attribute group decision making with linguistic information is developed based on the TCHFEWA and the TCHFEHWA operators. Furthermore, we establish various properties of these operators and derive the relationship between the proposed operators and the existing aggregation operators. Finally, a numerical example is provided to demonstrate the application of the established approach. Full article

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14 pages, 828 KiB

Open AccessArticle

An Integrated Decision Framework for Material Selection Procedure: A Case Study in a Detergent Manufacturer

by Mehtap Dursun^* and Özlem Arslan

Industrial Engineering Department, Galatasaray University, Faculty of Engineering and Technology, Ortakoy, Istanbul 34349, Turkey

Symmetry 2018, 10(11), 657; https://doi.org/10.3390/sym10110657 - 20 Nov 2018

Cited by 16 | Viewed by 3369

Abstract

The new product development process (NPD) is considered to be the key factor of competition among different markets. The identification of a suitable material is an important issue in the conception and improvement of new products. Material selection is seen as an important [...] Read more.

The new product development process (NPD) is considered to be the key factor of competition among different markets. The identification of a suitable material is an important issue in the conception and improvement of new products. Material selection is seen as an important multi-criteria decision making (MCDM) problem in engineering because of the requirement of considering multiple criteria from different dimensions. Improper material selection may negatively affect the success of a firm. The purpose of this study is to specify the importance of selection attributes, which are considered to evaluate washing liquid that meets the needs of both customers and firms. Then, it objects to choose the most appropriate alternative among various formulations. A fuzzy MCDM methodology based on quality function deployment (QFD), 2-tuple fuzzy linguistic representation, and linguistic hierarchies is presented. QFD is used to incorporate customer requirements into the evaluation process. The 2-tuple fuzzy modeling and linguistic hierarchies are employed to combine multi-granular data given by experts. Finally, the fuzzy COPRAS (Complex Proportional Assessment) method is used to choose the most suitable alternative. The implementation of the developed method is presented by a case study conducted on a detergent manufacturer located in Turkey. Full article

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11 pages, 271 KiB

Open AccessArticle

Neutrosophic Logic Based Quantum Computing

by Ahmet Çevik¹

, Selçuk Topal^2,*

and Florentin Smarandache³

¹ Gendarmerie and Coast Guard Academy, Department of Science, Ankara 06805, Turkey

² Department of Mathematics, Faculty of Science and Arts, Bitlis Eren University, Bitlis 13000, Turkey

³ Department of Mathematics, University of New Mexico, Gallup, NM 87301, USA

Symmetry 2018, 10(11), 656; https://doi.org/10.3390/sym10110656 - 20 Nov 2018

Cited by 6 | Viewed by 3929

Abstract

We introduce refined concepts for neutrosophic quantum computing such as neutrosophic quantum states and transformation gates, neutrosophic Hadamard matrix, coherent and decoherent superposition states, entanglement and measurement notions based on neutrosophic quantum states. We also give some observations using these principles. We present [...] Read more.

We introduce refined concepts for neutrosophic quantum computing such as neutrosophic quantum states and transformation gates, neutrosophic Hadamard matrix, coherent and decoherent superposition states, entanglement and measurement notions based on neutrosophic quantum states. We also give some observations using these principles. We present a number of quantum computational matrix transformations based on neutrosophic logic and clarify quantum mechanical notions relying on neutrosophic states. The paper is intended to extend the work of Smarandache by introducing a mathematical framework for neutrosophic quantum computing and presenting some results. Full article

(This article belongs to the Special Issue Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets)

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13 pages, 622 KiB

Open AccessArticle

New Constructions of Quantum Stabilizer Codes Based on Difference Sets

by Duc Manh Nguyen

and Sunghwan Kim^*

School of Electrical Engineering, University of Ulsan, Ulsan 44610, Korea

Symmetry 2018, 10(11), 655; https://doi.org/10.3390/sym10110655 - 19 Nov 2018

Cited by 12 | Viewed by 4236

Abstract

In this paper, new conditions on parameters in difference sets are derived to satisfy symplectic inner product, and new constructions of quantum stabilizer codes are proposed from the conditions. The conversion of the difference sets into parity-check matrices is first explained. Then, the [...] Read more.

In this paper, new conditions on parameters in difference sets are derived to satisfy symplectic inner product, and new constructions of quantum stabilizer codes are proposed from the conditions. The conversion of the difference sets into parity-check matrices is first explained. Then, the proposed code construction is composed of three steps, which are to choose the generators of quantum stabilizer code, to determine the quantum stabilizer groups, and to determine subspace codewords with large minimum distance. The quantum stabilizer codes with various length are also presented to explain the practicality of the code construction. The proposed design can be applied to quantum stabilizer code construction based on combinatorial design. Full article

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26 pages, 2311 KiB

Open AccessArticle

Online Social Networks (OSN) Evolution Model Based on Homophily and Preferential Attachment

by Jebran Khan

and Sungchang Lee^*

School of Electronics and Information Engineering, Korea Aerospace University, Deogyang-gu, Goyang-si, Gyeonggi-do 412-791, Korea

Symmetry 2018, 10(11), 654; https://doi.org/10.3390/sym10110654 - 19 Nov 2018

Cited by 8 | Viewed by 6567

Abstract

In this paper, we propose a new scale-free social networks (SNs) evolution model that is based on homophily combined with preferential attachments. Our model enables the SN researchers to generate SN synthetic data for the evaluation of multi-facet SN models that are dependent [...] Read more.

In this paper, we propose a new scale-free social networks (SNs) evolution model that is based on homophily combined with preferential attachments. Our model enables the SN researchers to generate SN synthetic data for the evaluation of multi-facet SN models that are dependent on users’ attributes and similarities. Homophily is one of the key factors for interactive relationship formation in SN. The synthetic graph generated by our model is scale-invariant and has symmetric relationships. The model is dynamic and sustainable to changes in input parameters, such as number of nodes and nodes’ attributes, by conserving its structural properties. Simulation and evaluation of models for large-scale SN applications need large datasets. One way to get SN data is to generate synthetic data by using SN evolution models. Various SN evolution models are proposed to approximate the real-life SN graphs in previous research. These models are based on SN structural properties such as preferential attachment. The data generated by these models is suitable to evaluate SN models that are structure dependent but not suitable to evaluate models which depend on the SN users’ attributes and similarities. In our proposed model, users’ attributes and similarities are utilized to synthesize SN graphs. We evaluated the resultant synthetic graph by analyzing its structural properties. In addition, we validated our model by comparing its measures with the publicly available real-life SN datasets and previous SN evolution models. Simulation results show our resultant graph to be a close representation of real-life SN graphs with users’ attributes. Full article

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16 pages, 289 KiB

Open AccessArticle

Design of a New Synthetic Acceptance Sampling Plan

by Saeed A. Dobbah, Muhammad Aslam^*

and Khushnoor Khan

Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21551, Saudi Arabia

Symmetry 2018, 10(11), 653; https://doi.org/10.3390/sym10110653 - 19 Nov 2018

Cited by 10 | Viewed by 2579

Abstract

In this paper, we propose a new synthetic sampling plan assuming that the quality characteristic follows the normal distribution with known and unknown standard deviation. The proposed plan is given and the operating characteristic (OC) function is derived to measure the performance of [...] Read more.

In this paper, we propose a new synthetic sampling plan assuming that the quality characteristic follows the normal distribution with known and unknown standard deviation. The proposed plan is given and the operating characteristic (OC) function is derived to measure the performance of the proposed sampling plan for some fixed parameters. The parameters of the proposed sampling plan are determined using non-linear optimization solution. A real example is added to explain the use of the proposed plan by industry. Full article

16 pages, 284 KiB

Open AccessArticle

A New Class of Hermite-Apostol Type Frobenius-Euler Polynomials and Its Applications

by Serkan Araci^1,*

, Mumtaz Riyasat², Shahid Ahmad Wani²

and Subuhi Khan²

¹ Department of Economics, Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu University, Gaziantep TR-27410, Turkey

² Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh 202 002, India

Symmetry 2018, 10(11), 652; https://doi.org/10.3390/sym10110652 - 19 Nov 2018

Cited by 7 | Viewed by 3260

Abstract

The article is written with the objectives to introduce a multi-variable hybrid class, namely the Hermite–Apostol-type Frobenius–Euler polynomials, and to characterize their properties via different generating function techniques. Several explicit relations involving Hurwitz–Lerch Zeta functions and some summation formulae related to these polynomials [...] Read more.

The article is written with the objectives to introduce a multi-variable hybrid class, namely the Hermite–Apostol-type Frobenius–Euler polynomials, and to characterize their properties via different generating function techniques. Several explicit relations involving Hurwitz–Lerch Zeta functions and some summation formulae related to these polynomials are derived. Further, we establish certain symmetry identities involving generalized power sums and Hurwitz–Lerch Zeta functions. An operational view for these polynomials is presented, and corresponding applications are given. The illustrative special cases are also mentioned along with their generating equations. Full article

(This article belongs to the Special Issue Current Trends in Symmetric Polynomials with their Applications)

19 pages, 602 KiB

Open AccessArticle

Comparison of Random Subspace and Voting Ensemble Machine Learning Methods for Face Recognition

by Mehmet Akif Yaman^1,*, Abdulhamit Subasi²

and Frank Rattay¹

¹ Institute for Analysis and Scientific Computing, Vienna University of Technology, Vienna 1040, Austria

² College of Engineering, Effat University, Jeddah 21478, Saudi Arabia

Symmetry 2018, 10(11), 651; https://doi.org/10.3390/sym10110651 - 19 Nov 2018

Cited by 45 | Viewed by 6155

Abstract

Biometry based authentication and recognition have attracted greater attention due to numerous applications for security-conscious societies, since biometrics brings accurate and consistent identification. Face biometry possesses the merits of low intrusiveness and high precision. Despite the presence of several biometric methods, like iris [...] Read more.

Biometry based authentication and recognition have attracted greater attention due to numerous applications for security-conscious societies, since biometrics brings accurate and consistent identification. Face biometry possesses the merits of low intrusiveness and high precision. Despite the presence of several biometric methods, like iris scan, fingerprints, and hand geometry, the most effective and broadly utilized method is face recognition, because it is reasonable, natural, and non-intrusive. Face recognition is a part of the pattern recognition that is applied for identifying or authenticating a person that is extracted from a digital image or a video automatically. Moreover, current innovations in big data analysis, cloud computing, social networks, and machine learning have allowed for a straightforward understanding of how different challenging issues in face recognition might be solved. Effective face recognition in the enormous data concept is a crucial and challenging task. This study develops an intelligent face recognition framework that recognizes faces through efficient ensemble learning techniques, which are Random Subspace and Voting, in order to improve the performance of biometric systems. Furthermore, several methods including skin color detection, histogram feature extraction, and ensemble learner-based face recognition are presented. The proposed framework, which has a symmetric structure, is found to have high potential for biometrics. Hence, the proposed framework utilizing histogram feature extraction with Random Subspace and Voting ensemble learners have presented their superiority over two different databases as compared with state-of-art face recognition. This proposed method has reached an accuracy of 99.25% with random forest, combined with both ensemble learners on the FERET face database. Full article

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20 pages, 1859 KiB

Open AccessArticle

An Enhanced Approach for the Multiple Vehicle Routing Problem with Heterogeneous Vehicles and a Soft Time Window

by He-Yau Kang¹

and Amy H. I. Lee^2,*

¹ Department of Industrial Engineering and Management, National Chin-Yi University of Technology, Taichung 411, Taiwan

² Department of Technology Management, Chung Hua University, Hsinchu 300, Taiwan

Symmetry 2018, 10(11), 650; https://doi.org/10.3390/sym10110650 - 19 Nov 2018

Cited by 24 | Viewed by 7911

Abstract

The vehicle routing problem (VRP) is a challenging combinatorial optimization problem. This research focuses on the problem under which a manufacturer needs to outsource materials from other suppliers and to ship the materials back to the company. Heterogeneous vehicles are available to ship [...] Read more.

The vehicle routing problem (VRP) is a challenging combinatorial optimization problem. This research focuses on the problem under which a manufacturer needs to outsource materials from other suppliers and to ship the materials back to the company. Heterogeneous vehicles are available to ship the materials, and each vehicle has a limited loading capacity and a limited travelling distance. The purpose of this research is to study a multiple vehicle routing problem (MVRP) with soft time window and heterogeneous vehicles. Two models, using mixed integer programming (MIP) and genetic algorithm (GA), are developed to solve the problem. The MIP model is first constructed to minimize the total transportation cost, which includes the assignment cost, travelling cost, and the tardiness cost, for the manufacturer. The optimal solution can present multiple vehicle routing and the loading size of each vehicle in each period. The GA is next applied to solve the problem so that a near-optimal solution can be obtained when the problem is too difficult to be solved using the MIP. A case of a food manufacturing company is used to examine the practicality of the proposed MIP model and the GA model. The results show that the MIP model can obtain the optimal solution under a short computational time when the scale of the problem is small. When the problem becomes non-deterministic polynomial hard (NP-hard), the MIP model cannot find the optimal solution. On the other hand, the GA model can obtain a near-optimal solution within a reasonable amount of computational time. This paper is related to several important topics of the Symmetry journal in the areas of mathematics and computer science theory and methods. In the area of mathematics, the theories of linear and non-linear algebraic structures and information technology are adopted. In the area of computer science, theory and methods, and metaheuristics are applied. Full article

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11 pages, 955 KiB

Open AccessArticle

The Influence of Organs on Biochemical Properties of Tunisian Thuja occidentalis Essential Oils

by Sana Bellili^1,2, Chedia Aouadhi³, Wissal Dhifi⁴, Hanene Ghazghazi⁵, Chaima Jlassi¹, Carmen Sadaka⁶

, Marc El Beyrouthy⁷, Abderrazak Maaroufi³, Ameur Cherif¹ and Wissem Mnif^1,8,*

¹ LR11-ES31 Laboratory of Biotechnology and Valorisation of Bio-GeoRessources, Higher Institute of Biotechnology of Sidi Thabet, BiotechPole of SidiThabet, University of Manouba, Ariana 2020, Tunisia

² Faculty of Sciences of Bizerte, Jarzouna-Bizerte, University of Carthage, Zarzouna 7021, Tunisia

³ Laboratory of Epidemiology and Veterinary Microbiology, Bacteriology and Development Biotechnology Groups, Pasteur Institute of Tunisia, University of Manar, Tunis 1002, Tunisia

⁴ LR17-ES03 Physiopathology, Food and Biomolecules, Higher Institute of Biotechnology of Sidi Thabet, Biotechpole Sidi Thabet, Ariana 2020, Tunisia

⁵ Laboratory of Management and Valorization of Forest Resources, National Research Institute of Rural Engineering, Water and Forestry (INRGREF), Tunis 1002, Tunisia

⁶ Department of Veterinary and Animal Sciences, University of Copenhagen, Stigboejlen 4, 1870 Frederiksberg, Denmark

⁷ Holy Spirit University of Kaslik, P.O. Box 446 Jounieh, Mount Lebanon, Lebanon

⁸ Faculty of Sciences and Arts in Balgarn, University of Bisha, Kingdom of Saudi Arabia, P.O. BOX 60 Balgarn, Sabt Al Alaya 61985, Saudi Arabia

Symmetry 2018, 10(11), 649; https://doi.org/10.3390/sym10110649 - 19 Nov 2018

Cited by 13 | Viewed by 4670

Abstract

In this study, the chemical composition and biological activities of the essential oil (EO) extracts (from leaves and cones) of the Tunisian Thuja occidentalis were evaluated. The composition of the leaf EO extract was more complex than that of the cones. The major [...] Read more.

In this study, the chemical composition and biological activities of the essential oil (EO) extracts (from leaves and cones) of the Tunisian Thuja occidentalis were evaluated. The composition of the leaf EO extract was more complex than that of the cones. The major components of the leaf EO extract were α-Pinene (34.4%), cedrol (13.17%), and β-Phellandrene (8.04%), while the composition of the cone EO extract was characterized by the predominance of α-Pinene (58.55%) and 3-Carene (24.08%). All EO extracts showed much better antioxidant activity than Trolox against 2, 2′-diphenyl-1-picryl hydrazyl (DPPH) radical scavenging, but EOs extracted from leaves exhibited the highest total antioxidant activity. All EOs showed strong antibacterial and antifungal activities against nine tested foodborne microorganisms (Bacillus cereus American Type Culture Collection (ATCC) 1247, Listeria monocytogenes ATCC 7644, Staphylococcus aureus ATCC 29213, Aeromonas hydrophila EI, Escherichia coli ATCC 8739, Pseudomonas aeruginosa ATCC 27853, Salmonella typhimurium NCTC 6017, Aspergillus flavus (foodborne isolate), and Aspergillus niger CTM 10099. The highest antimicrobial activities by disk diffusion assay were recorded for the EOs extracted from leaves, while no difference in potency was marked between leaf and cone EO extracts by the agar dilution method. The most potent antimicrobial activity was recorded among fungi. This study confirms the strong antimicrobial and antioxidant potential of EO extracts from the Tunisian T. occidentalis (from the Sidi Bou Said site), highlighting its potential as a natural preservative against foodborne pathogens, particularly against E. coli and S. typhimurium. Full article

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18 pages, 7155 KiB

Open AccessArticle

A Comparison of Regularization Techniques in Deep Neural Networks

by Ismoilov Nusrat¹ and Sung-Bong Jang^2,*

¹ Department of Computer Software Engineering, Kumoh National Institute of Technology, Gyeong-Buk 39177, South Korea

² Department of Industry-Academy, Kumoh National Institute of Technology, Gyeong-Buk 39177, South Korea

Symmetry 2018, 10(11), 648; https://doi.org/10.3390/sym10110648 - 18 Nov 2018

Cited by 82 | Viewed by 13394

Abstract

Artificial neural networks (ANN) have attracted significant attention from researchers because many complex problems can be solved by training them. If enough data are provided during the training process, ANNs are capable of achieving good performance results. However, if training data are not [...] Read more.

Artificial neural networks (ANN) have attracted significant attention from researchers because many complex problems can be solved by training them. If enough data are provided during the training process, ANNs are capable of achieving good performance results. However, if training data are not enough, the predefined neural network model suffers from overfitting and underfitting problems. To solve these problems, several regularization techniques have been devised and widely applied to applications and data analysis. However, it is difficult for developers to choose the most suitable scheme for a developing application because there is no information regarding the performance of each scheme. This paper describes comparative research on regularization techniques by evaluating the training and validation errors in a deep neural network model, using a weather dataset. For comparisons, each algorithm was implemented using a recent neural network library of TensorFlow. The experiment results showed that an autoencoder had the worst performance among schemes. When the prediction accuracy was compared, data augmentation and the batch normalization scheme showed better performance than the others. Full article

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19 pages, 481 KiB

Open AccessArticle

Transceiver Design and Power Allocation for SWIPT in MIMO Cognitive Radio Systems

by Fahui Wu¹, Lin Xiao^2,*, Dingcheng Yang², Laurie Cuthbert³

and Xiaoping Liu^1,4

¹ Jiangxi Province Key Laboratory of Intelligent Information Systems, Nanchang University, Nanchang 330031, China

² Information Engineering School, Nanchang University, Nanchang 330031, China

³ Information Systems Research Centre, Macao Polytechnic Institute, Macao 999078, China

⁴ Department of Systems and Computer Engineering, Carleton University, Ottawa, ON K1S 5B6, Canada

Symmetry 2018, 10(11), 647; https://doi.org/10.3390/sym10110647 - 18 Nov 2018

Cited by 4 | Viewed by 3510

Abstract

In this paper, we consider a symmetric wireless communication network, i.e., each user is equipped with the same number of antennas. Specifically, this paper studies simultaneous wireless information and power transfer (SWIPT) in a K-user multiple-input multiple-output (MIMO) cognitive radio network where [...] Read more.

In this paper, we consider a symmetric wireless communication network, i.e., each user is equipped with the same number of antennas. Specifically, this paper studies simultaneous wireless information and power transfer (SWIPT) in a K-user multiple-input multiple-output (MIMO) cognitive radio network where the secondary users (SUs) access the same frequency band as the pre-existing primary user (PU) without generating any interference. The transceivers and power splitting ratio are designed and power allocation is considered in our system model. To guarantee the signal-to-interference-plus-noise ratio (SINR) and harvested energy requirement of the PU, its optimal transceiver and minimal transmitted power are obtained by the technique of semi-definite relaxation (SDR). We design the beamformers of the SUs using the distance between the interference subspaces at the PU and the null space of PU’s desired signal to preserve the PU from the interference caused by the SUs. We aim to maximize the sum rate of all the SUs by jointly designing power splitting ratios and allocating transmission power. Furthermore, to consider the performance fairness of SUs, we propose another approach to maximize the minimum SINR of the SUs. Finally, numerical results are given to evaluate the performance of proposed approaches. Full article

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21 pages, 5637 KiB

Open AccessArticle

A Q-Learning-Based Approach for Deploying Dynamic Service Function Chains

by Jian Sun¹, Guanhua Huang¹, Gang Sun^1,2,*

, Hongfang Yu^1,2, Arun Kumar Sangaiah³

and Victor Chang⁴

¹ Key Lab of Optical Fiber Sensing and Communications (Ministry of Education), University of Electronic Science and Technology of China, Chengdu 611731, China

² Center for Cyber Security, University of Electronic Science and Technology of China, Chengdu 611731, China

³ School of Computing Science and Engineering, Vellore Institute of Technology, Tamil Nadu 632014, India

⁴ International Business School Suzhou (IBSS), Xi’an Jiaotong-Liverpool University, Suzhou 215123, China

Symmetry 2018, 10(11), 646; https://doi.org/10.3390/sym10110646 - 16 Nov 2018

Cited by 33 | Viewed by 5121

Abstract

As the size and service requirements of today’s networks gradually increase, large numbers of proprietary devices are deployed, which leads to network complexity, information security crises and makes network service and service provider management increasingly difficult. Network function virtualization (NFV) technology is one [...] Read more.

As the size and service requirements of today’s networks gradually increase, large numbers of proprietary devices are deployed, which leads to network complexity, information security crises and makes network service and service provider management increasingly difficult. Network function virtualization (NFV) technology is one solution to this problem. NFV separates network functions from hardware and deploys them as software on a common server. NFV can be used to improve service flexibility and isolate the services provided for each user, thus guaranteeing the security of user data. Therefore, the use of NFV technology includes many problems worth studying. For example, when there is a free choice of network path, one problem is how to choose a service function chain (SFC) that both meets the requirements and offers the service provider maximum profit. Most existing solutions are heuristic algorithms with high time efficiency, or integer linear programming (ILP) algorithms with high accuracy. It’s necessary to design an algorithm that symmetrically considers both time efficiency and accuracy. In this paper, we propose the Q-learning Framework Hybrid Module algorithm (QLFHM), which includes reinforcement learning to solve this SFC deployment problem in dynamic networks. The reinforcement learning module in QLFHM is responsible for the output of alternative paths, while the load balancing module in QLFHM is responsible for picking the optimal solution from them. The results of a comparison simulation experiment on a dynamic network topology show that the proposed algorithm can output the approximate optimal solution in a relatively short time while also considering the network load balance. Thus, it achieves the goal of maximizing the benefit to the service provider. Full article

(This article belongs to the Special Issue Symmetry-Adapted Machine Learning for Information Security)

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25 pages, 6034 KiB

Open AccessArticle

Geometrical Information Flow Regulated by Time Lengths: An Initial Approach

by Charles Roberto Telles

Administrative Sectorial Group, Continuous Services Sector, Secretary of State for Education of Paraná, Curitiba 80240-070, Brazil

Symmetry 2018, 10(11), 645; https://doi.org/10.3390/sym10110645 - 16 Nov 2018

Cited by 4 | Viewed by 4289

Abstract

The article analyzes Bernoulli’s binary sequences in the representation of empirical events about water usage and continuous expenditure systems. The main purpose is to identify among variables that constitute water resources consumption at public schools, the link between consumption and expenditures oscillations. It [...] Read more.

The article analyzes Bernoulli’s binary sequences in the representation of empirical events about water usage and continuous expenditure systems. The main purpose is to identify among variables that constitute water resources consumption at public schools, the link between consumption and expenditures oscillations. It was obtained a theoretical model of how oscillations patterns are originated and how time lengths have an important role over expenditures oscillations ergodicity and non-ergodicity. Full article

(This article belongs to the Special Issue Solution Models based on Symmetric and Asymmetric Information)

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18 pages, 2167 KiB

Open AccessArticle

Characterization of HIV-2 Protease Structure by Studying Its Asymmetry at the Different Levels of Protein Description

by Guillaume Ollitrault¹, Sandrine Fartek¹, Diane Descamps², Anne-Claude Camproux¹

, Benoît Visseaux²

and Leslie Regad^1,*

¹ Molécules thérapeutiques in silico (MTi), UMR-S973, Université Paris Diderot, Sorbonne Paris Cité, INSERM, F-75013 Paris, France

² Infection, Antimicrobiens, Modélisation, Evolution (IAME), UMR 1137, Université Paris Diderot, Sorbonne Paris Cité, INSERM, AP-HP, Hôpital Bichat, Virologie, 75018 Paris, France

Symmetry 2018, 10(11), 644; https://doi.org/10.3390/sym10110644 - 16 Nov 2018

Cited by 4 | Viewed by 3575

Abstract

HIV-2 protease (PR2) is a homodimer, which is an important target in the treatment of the HIV-2 infection. In this study, we developed an in silico protocol to analyze and characterize the asymmetry of the unbound PR2 structure using three levels of protein [...] Read more.

HIV-2 protease (PR2) is a homodimer, which is an important target in the treatment of the HIV-2 infection. In this study, we developed an in silico protocol to analyze and characterize the asymmetry of the unbound PR2 structure using three levels of protein description by comparing the conformation, accessibility, and flexibility of each residue in the two PR2 chains. Our results showed that 65% of PR2 residues have at least one of the three studied asymmetries (structural, accessibility, or flexibility) with 10 positions presenting the three asymmetries in the same time. In addition, we noted that structural and flexibility asymmetries are linked indicating that the structural asymmetry of some positions result from their large flexibility. By comparing the structural asymmetry of the crystallographic and energetically minimized structures of the unbound PR2, we confirmed that the structural asymmetry of unbound PR2 is an intrinsic property of this protein with an important role for the PR2 deformation upon ligand binding. This analysis also allowed locating asymmetries corresponding to crystallization artefacts. This study provides insight that will help to better understand the structural deformations of PR2 and to identify key positions for ligand binding. Full article

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9 pages, 306 KiB

Open AccessFeature PaperArticle

Neutrosophic Computability and Enumeration

by Ahmet Çevik¹

, Selçuk Topal^2,*

and Florentin Smarandache³

¹ Gendarmerie and Coast Guard Academy, Department of Science, 06805 Ankara, Turkey, a.cevik@hotmail.com

² Department of Mathematics, Faculty of Science and Arts, Bitlis Eren University, 13000 Bitlis, Turkey

³ Department of Mathematics, University of New Mexico, Gallup, NM 87301, USA

Symmetry 2018, 10(11), 643; https://doi.org/10.3390/sym10110643 - 16 Nov 2018

Cited by 3 | Viewed by 3004

Abstract

We introduce oracle Turing machines with neutrosophic values allowed in the oracle information and then give some results when one is permitted to use neutrosophic sets and logic in relative computation. We also introduce a method to enumerate the elements of a neutrosophic [...] Read more.

We introduce oracle Turing machines with neutrosophic values allowed in the oracle information and then give some results when one is permitted to use neutrosophic sets and logic in relative computation. We also introduce a method to enumerate the elements of a neutrosophic subset of natural numbers. Full article

(This article belongs to the Special Issue Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets)

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14 pages, 1649 KiB

Open AccessArticle

Fuzzy AHP Application for Supporting Contractors’ Bidding Decision

by Agnieszka Leśniak^*

, Daniel Kubek

, Edyta Plebankiewicz

, Krzysztof Zima

and Stanisław Belniak

Cracow University of Technology, Faculty of Civil Engineering, 31-155 Kraków, Poland

Symmetry 2018, 10(11), 642; https://doi.org/10.3390/sym10110642 - 16 Nov 2018

Cited by 75 | Viewed by 8589

Abstract

This paper proposes the author’s model based on the Fuzzy Analytic Hierarchy Process (FAHP) to improve the efficiency of contractor bidding decisions. The essence of the AHP method is to make pairwise comparisons of available options against all evaluation criteria. The results of [...] Read more.

This paper proposes the author’s model based on the Fuzzy Analytic Hierarchy Process (FAHP) to improve the efficiency of contractor bidding decisions. The essence of the AHP method is to make pairwise comparisons of available options against all evaluation criteria. The results of these comparisons are recorded in a square matrix in which symmetrical elements are reciprocal. In the expert opinion, a 9-step, bipolar verbal scale was used so that the symmetry of the response was maintained. For contractors from countries where the tendering system is commonly used, the choice of the right tender in which to participate influences their image, financial condition, and their aspiration to succeed. The bid/no bid decision depends on numerous factors associated with the company itself, the environment, and the project concerning the tender. When facing tough competition, contractors search for a solution which increases their chances of winning the tender. The proposed model was based on factors selected by Polish contractors. The original element of the model involves 4 original criteria and 15 sub-criteria for the assessment of investment decision projects to the selection of the most advantageous contract, i.e., the contractor’s participation in the bid. For verbal evaluations describing the criteria, symmetric triangular fuzzy numbers were assigned. The authors performed an extended analysis method combined with FAHP in the model. Fuzzy evaluations underwent elaborate analysis, the aim of which was to specify the synthetic priority weights for each criterion. As a result of the application of the method, to prove that the model works, an example from the Polish construction market was presented in which a bid/no bid decision about four possible tenders was to be taken. Despite the considered example applying to Polish conditions, the proposed model can be used also in other countries. The authors’ rationale is to produce new and more flexible methodologies in order to realistically model a variety of concrete decision problems. Full article

(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)

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9 pages, 723 KiB

Open AccessArticle

Design of a New Variable Shewhart Control Chart Using Multiple Dependent State Repetitive Sampling

by Mansour Sattam Aldosari¹, Muhammad Aslam^1,*

, Nasrullah Khan²

and Chi-Hyuck Jun³

¹ Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21551, Saudi Arabia

² Department of Statistics, Jhang Campus, University of Veterinary and Animal Sciences, Lahore 54000, Pakistan

³ Department of Industrial and Management Engineering, Pohang University of Science and Technology, Pohang 37673, Korea

Symmetry 2018, 10(11), 641; https://doi.org/10.3390/sym10110641 - 15 Nov 2018

Cited by 7 | Viewed by 3107

Abstract

In this paper, a new variable control chart is proposed using multiple dependent-state repetitive sampling by assuming that the data follows a normal distribution having a symmetry property. Its efficiency will be evaluated in terms of in-control and out-of-control average run lengths. The [...] Read more.

In this paper, a new variable control chart is proposed using multiple dependent-state repetitive sampling by assuming that the data follows a normal distribution having a symmetry property. Its efficiency will be evaluated in terms of in-control and out-of-control average run lengths. The results showed that the proposed chart is better than the existing variable control chart to detect an early shift in the process. An industrial example is given to illustrate the proposed chart in the industry. Full article

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15 pages, 869 KiB

Open AccessArticle

Simplified Neutrosophic Sets Based on Interval Dependent Degree for Multi-Criteria Group Decision-Making Problems

by Libo Xu^1,*

, Xingsen Li², Chaoyi Pang¹ and Yan Guo¹

¹ Department of Computer and Data Engineering, Zhejiang University Ningbo Institute of Technology, Ningbo 315000, China

² Research Institute of Extenics and Innovation Methods, Guangdong University of Technology, Guangzhou 510000, China

Symmetry 2018, 10(11), 640; https://doi.org/10.3390/sym10110640 - 15 Nov 2018

Cited by 7 | Viewed by 3894

Abstract

In this paper, a new approach and framework based on the interval dependent degree for multi-criteria group decision-making (MCGDM) problems with simplified neutrosophic sets (SNSs) is proposed. Firstly, the simplified dependent function and distribution function are defined. Then, they are integrated into the [...] Read more.

In this paper, a new approach and framework based on the interval dependent degree for multi-criteria group decision-making (MCGDM) problems with simplified neutrosophic sets (SNSs) is proposed. Firstly, the simplified dependent function and distribution function are defined. Then, they are integrated into the interval dependent function which contains interval computing and distribution information of the intervals. Subsequently, the interval transformation operator is defined to convert simplified neutrosophic numbers (SNNs) into intervals, and then the interval dependent function for SNNs is deduced. Finally, an example is provided to verify the feasibility and effectiveness of the proposed method, together with its comparative analysis. In addition, uncertainty analysis, which can reflect the dynamic change of the final result caused by changes in the decision makers’ preferences, is performed in different distribution function situations. That increases the reliability and accuracy of the result. Full article

(This article belongs to the Special Issue Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets)

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18 pages, 1762 KiB

Open AccessArticle

The Augmented Approach towards Equilibrated Nexus Era into the Wireless Rechargeable Sensor Network

by Ahmad Ali^1,*

, Yu Ming^1,*, Sagnik Chakraborty², Saima Iram² and Tapas Si³

¹ School of Electronics and Information Engineering, Hebei University of Technology, Tianjin 300401, China

² School of Energy and Environmental Engineering, Hebei University of Technology, Tianjin 300401, China

³ Department of Computer Science and Engineering, Bankura Unnayani Institute of Engineering, Bankura 722146, India

Symmetry 2018, 10(11), 639; https://doi.org/10.3390/sym10110639 - 15 Nov 2018

Cited by 1 | Viewed by 3216

Abstract

Present research in the domain of wireless sensor network (WSN) has unearthed that energy restraint of sensor nodes (SNs) encumbers their perpetual performance. Of late, the encroachment in the vicinity of wireless power transfer (WPT) technology has achieved pervasive consideration from both industry [...] Read more.

Present research in the domain of wireless sensor network (WSN) has unearthed that energy restraint of sensor nodes (SNs) encumbers their perpetual performance. Of late, the encroachment in the vicinity of wireless power transfer (WPT) technology has achieved pervasive consideration from both industry and academia to cater the sensor nodes (SNs) letdown in the wireless rechargeable sensor network (WRSNs). The fundamental notion of wireless power transfer is to replenish the energy of sensor nodes using a single or multiple wireless charging devices (WCDs). Herein, we present a jointly optimization model to maximize the charging efficiency and routing restraint of the wireless charging device (WCD). At the outset, we intend an unswerving charging path algorithm to compute the charging path of the wireless charging device. Moreover, Particle swarm optimization (PSO) algorithm has designed with the aid of a virtual clustering technique during the routing process to equilibrate the network lifetime. Herein clustering algorithm, the enduring energy of the sensor nodes is an indispensable parameter meant for the assortment of cluster head (CH). Furthermore, compare the proposed approach to corroborate its pre-eminence over the benchmark algorithm in diverse scenarios. The simulation results divulge that the proposed work is enhanced concerning the network lifetime, charging performance and the enduring energy of the sensor nodes. Full article

(This article belongs to the Special Issue Information Technology and Its Applications 2021)

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16 pages, 3001 KiB

Open AccessArticle

Construction and Simulation of Composite Measures and Condensation Model for Designing Probabilistic Computational Applications

by Susmit Bagchi

Department of Aerospace and Software Engineering (Informatics), Gyeongsang National University, Jinju 660701, Korea

Symmetry 2018, 10(11), 638; https://doi.org/10.3390/sym10110638 - 15 Nov 2018

Viewed by 2787

Abstract

The probabilistic algorithms are widely applied in designing computational applications such as distributed systems and probabilistic databases, to determine distributed consensus in the presence of random failures of nodes or networks. In distributed computing, symmetry breaking is performed by employing probabilistic algorithms. In [...] Read more.

The probabilistic algorithms are widely applied in designing computational applications such as distributed systems and probabilistic databases, to determine distributed consensus in the presence of random failures of nodes or networks. In distributed computing, symmetry breaking is performed by employing probabilistic algorithms. In general, probabilistic symmetry breaking without any bias is preferred. Thus, the designing of randomized and probabilistic algorithms requires modeling of associated probability spaces to generate control-inputs. It is required that discrete measures in such spaces are computable and tractable in nature. This paper proposes the construction of composite discrete measures in real as well as complex metric spaces. The measures are constructed on different varieties of continuous smooth curves having distinctive non-linear profiles. The compositions of discrete measures consider arbitrary functions within metric spaces. The measures are constructed on 1-D interval and 2-D surfaces and, the corresponding probability metric product is defined. The associated sigma algebraic properties are formulated. The condensation measure of the uniform contraction map is constructed as axioms. The computational evaluations of the proposed composite set of measures are presented. Full article

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18 pages, 338 KiB

Open AccessArticle

A Novel Vertical Fragmentation Method for Privacy Protection Based on Entropy Minimization in a Relational Database

by Tie Hong^1,†,‡, SongZhu Mei^2,*,‡, ZhiYing Wang^1,‡ and JiangChun Ren^1,‡

¹ College of Computer, National University of Defense Technology, Changsha 410073, China

² Science and Technology on Parallel and Distributed Laboratory, National University of Defense Technology, Changsha 410073, China

^† Current address: The College of Computer, National University of Defense Technology, Changsha 410073, China.

^‡ These authors contributed equally to this work.

Symmetry 2018, 10(11), 637; https://doi.org/10.3390/sym10110637 - 14 Nov 2018

Cited by 2 | Viewed by 3037

Abstract

Many scholars have attempted to use an encryption method to resolve the problem of data leakage in data outsourcing storage. However, encryption methods reduce data availability and are inefficient. Vertical fragmentation perfectly solves this problem. It was first used to improve the access [...] Read more.

Many scholars have attempted to use an encryption method to resolve the problem of data leakage in data outsourcing storage. However, encryption methods reduce data availability and are inefficient. Vertical fragmentation perfectly solves this problem. It was first used to improve the access performance of the relational database, and nowadays some researchers employ it for privacy protection. However, there are some problems that remain to be solved with the vertical fragmentation method for privacy protection in the relational database. First, current vertical fragmentation methods for privacy protection require the user to manually define privacy constraints, which is difficult to achieve in practice. Second, there are many vertical fragmentation solutions that can meet privacy constraints; however, there are currently no quantitative evaluation criteria evaluating how effectively solutions can protect privacy more effectively. In this article, we introduce the concept of information entropy to quantify privacy in vertical fragmentation, so we can automatically discover privacy constraints. Based on this, we propose a privacy protection model with a minimum entropy fragmentation algorithm to achieve minimal privacy disclosure of vertical fragmentation. Experimental results show that our method is suitable for privacy protection with a lower overhead. Full article

(This article belongs to the Special Issue Information Technology and Its Applications 2021)

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29 pages, 1388 KiB

Open AccessArticle

m-Polar Fuzzy Soft Weighted Aggregation Operators and Their Applications in Group Decision-Making

by Azadeh Zahedi Khameneh¹

and Adem Kiliçman^1,2,*

¹ Institute for Mathematical Research, Universiti Putra Malaysia, UPM Serdang 43400, Selangor, Malaysia

² Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, UPM Serdang 43400, Selangor, Malaysia

Symmetry 2018, 10(11), 636; https://doi.org/10.3390/sym10110636 - 13 Nov 2018

Cited by 22 | Viewed by 3511

Abstract

Aggregation operators are important tools for solving multi-attribute group decision-making (MAGDM) problems. The main challenging issue for aggregating data in a MAGDM problem is how to develop a symmetric aggregation operator expressing the decision makers’ behavior. In the literature, there are some methods [...] Read more.

Aggregation operators are important tools for solving multi-attribute group decision-making (MAGDM) problems. The main challenging issue for aggregating data in a MAGDM problem is how to develop a symmetric aggregation operator expressing the decision makers’ behavior. In the literature, there are some methods dealing with this difficulty; however, they lack an effective approach for multi-polar inputs. In this study, a new aggregation operator for m-polar fuzzy soft sets (M-pFSMWM) reflecting different agreement scenarios within a group is presented to proceed MAGDM problems in which both attributes and experts have different weights. Moreover, some desirable properties of M-pFSMWM operator, such as idempotency, monotonicity, and commutativity (symmetric), that means being invariant under any permutation of the input arguments, are studied. Further, m-polar fuzzy soft induced ordered weighted average (M-pFSIOWA) operator and m-polar fuzzy soft induced ordered weighted geometric (M-pFSIOWG) operator, which are extensions of IOWA and IOWG operators, respectively, are developed. Two algorithms are also designed based on the proposed operators to find the final solution in MAGDM problems with weighted multi-polar fuzzy soft information. Finally, the efficiency of the proposed methods is illustrated by some numerical examples. The characteristic comparison of the proposed aggregation operators shows the M-pFSMWM operator is more adaptable for solving MAGDM problems in which different cases of agreement affect the final outcome. Full article

(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)

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15 pages, 758 KiB

Open AccessArticle

Tsallis, Rényi and Sharma-Mittal Holographic Dark Energy Models in Loop Quantum Cosmology

by Abdul Jawad¹

, Kazuharu Bamba^2,*, Muhammad Younas¹, Saba Qummer¹ and Shamaila Rani¹

¹ Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore-54000, Pakistan

² Division of Human Support System, Faculty of Symbiotic Systems Science, Fukushima University, Fukushima 960-1296, Japan

Symmetry 2018, 10(11), 635; https://doi.org/10.3390/sym10110635 - 13 Nov 2018

Cited by 54 | Viewed by 4774

Abstract

The cosmic expansion phenomenon is being studied through the interaction of newly proposed dark energy models (Tsallis, Rényi and Sharma-Mittal holographic dark energy (HDE) models) with cold dark matter in the framework of loop quantum cosmology. We investigate different cosmic implications such as [...] Read more.

The cosmic expansion phenomenon is being studied through the interaction of newly proposed dark energy models (Tsallis, Rényi and Sharma-Mittal holographic dark energy (HDE) models) with cold dark matter in the framework of loop quantum cosmology. We investigate different cosmic implications such as equation of state parameter, squared sound speed and cosmological plane (

ω_{d}

-

ω_{d}^{'}

,

ω_{d}

and

ω_{d}^{'}

represent the equation of state (EoS) parameter and its evolution, respectively). It is found that EoS parameter exhibits quintom like behavior of the universe for all three models of HDE. The squared speed of sound represents the stable behavior of Rényi HDE and Sharma-Mittal HDE at the latter epoch while unstable behavior for Tsallis HDE. Moreover,

ω_{d}

-

ω_{d}^{'}

plane lies in the thawing region for all three HDE models. Full article

(This article belongs to the Special Issue Cosmological Inflation, Dark Matter and Dark Energy)

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9 pages, 254 KiB

Open AccessFeature PaperArticle

Symmetric Properties of Carlitz’s Type q-Changhee Polynomials

by Yunjae Kim¹, Byung Moon Kim² and Jin-Woo Park^3,*

¹ Department of Mathematics, Dong-A University, Busan 49315, Korea

² Department of Mechanical System Engineering, Dongguk University, Gyeongju 38066, Korea

³ Department of Mathematics Education, Daegu University, Gyeongsan 38066, Korea

Symmetry 2018, 10(11), 634; https://doi.org/10.3390/sym10110634 - 13 Nov 2018

Cited by 1 | Viewed by 2868

Abstract

Changhee polynomials were introduced by Kim, and the generalizations of these polynomials have been characterized. In our paper, we investigate various interesting symmetric identities for Carlitz’s type q-Changhee polynomials under the symmetry group of order n arising from the fermionic p-adic [...] Read more.

Changhee polynomials were introduced by Kim, and the generalizations of these polynomials have been characterized. In our paper, we investigate various interesting symmetric identities for Carlitz’s type q-Changhee polynomials under the symmetry group of order n arising from the fermionic p-adic q-integral on

Z_{p}

. Full article

(This article belongs to the Special Issue Current Trends in Symmetric Polynomials with their Applications)

17 pages, 2221 KiB

Open AccessArticle

An Iterated Hybrid Local Search Algorithm for Pick-and-Place Sequence Optimization

by Jinsheng Gao¹

, Xiaomin Zhu¹, Anbang Liu¹, Qingyang Meng² and Runtong Zhang^2,*

¹ School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China

² School of Economics and Management, Beijing Jiaotong University, Beijing 100044, China

Symmetry 2018, 10(11), 633; https://doi.org/10.3390/sym10110633 - 13 Nov 2018

Cited by 10 | Viewed by 5480

Abstract

This paper shows the results of our study on the pick-and-place optimization problem. To solve this problem efficiently, an iterated hybrid local search algorithm (IHLS) which combines local search with integer programming is proposed. In the section of local search, the greedy algorithm [...] Read more.

This paper shows the results of our study on the pick-and-place optimization problem. To solve this problem efficiently, an iterated hybrid local search algorithm (IHLS) which combines local search with integer programming is proposed. In the section of local search, the greedy algorithm with distance weight strategy and the convex-hull strategy is developed to determine the pick-and-place sequence; in the section of integer programming, an integer programming model is built to complete the feeder assignment problem. The experimental results show that the IHLS algorithm we proposed has high computational efficiency. Furthermore, compared with the genetic algorithm and the memetic algorithm, the IHLS is less time-consuming and more suitable in solving a large-scale problem. Full article

(This article belongs to the Special Issue Symmetry in Computing Theory and Application)

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